Trace formula for a dielectric microdisk with a point scatterer

Abstract

Two-dimensional dielectric microcavities are of widespread use in microoptics applications. Recently, a trace formula has been established for dielectric cavities which relates their resonance spectrum to the periodic rays inside the cavity. In the present paper we extend this trace formula to a dielectric disk with a small scatterer. This system has been introduced for microlaser applications, because it has long-lived resonances with strongly directional far field. We show that its resonance spectrum contains signatures not only of periodic rays, but also of diffractive rays that occur in Keller's geometrical theory of diffraction. We compare our results with those for a closed cavity with Dirichlet boundary conditions.

39 pages, 18 figures, pdflatex

References in corpus (7)

• Inferring periodic orbits from spectra of simple shaped micro-lasers
• Trace formula for dielectric cavities II: Regular, pseudo-integrable, and chaotic examples
• Directional Emission from an Optical Microdisk Resonator with a Point Scatterer
• Experimental Test of a Two-dimensional Approximation for Dielectric Microcavities
• Resonances in a circular dielectric cavity
• Experimental test of a trace formula for two-dimensional dielectric resonators
• Diffractive orbits in the length spectrum of a 2D microwave cavity with a small scatterer

Cited by in corpus (7)

• Directional Emission of Dielectric Disks with a Finite Scatterer in the THz Regime
• Localized lasing modes of triangular organic microlasers
• Application of a trace formula to the spectra of flat three-dimensional dielectric resonators
• Trace formula for chaotic dielectric resonators tested with microwave experiments
• Dielectric Square Resonator Investigated with Microwave Experiments
• Spectral Properties and Dynamical Tunneling in Constant-Width Billiards
• Quality factors of deformed dielectric cavities